Fargher and Morse discuss the relationship between the four quality costs and explain how to minimize total quality costs
by analyzing these four cost functions. The authors argue that the traditional model of quality cost minimization assumes
that the manager has already identified the optimal combination of prevention and appraisal activities.
They begin by defining each of the four quality-related costs – prevention costs, appraisal cost, internal
failure costs, and external failure costs.

Prevention costs and appraisal costs are quality costs inputs.
These include costs incurred to produce a product that is not defective. Prevention costs are those costs associated with actions to ensure that
defects do not occur in initial production. Costs considered to be preventive in nature include costs to design a
higher quality product, training employees on quality activities, purchasing higher quality materials and increased maintenance on production equipment.
Appraisal costs, on the other hand, are cost incurred to test and inspect products in order to identify those products that do not meet specifications.
The greater the number of tests and inspections, the higher the appraisal costs and the more likely that a defective unit will be
identified. Many companies may find that identifying 100% of defective units is very costly, with costs rising
sharply as the proportion of defects found approaches 100%.

Internal and external failure costs are considered the quality cost outputs. Internal failure occurs when a
product is found to be defective before reaching the customer while external failure occurs when a defect is found after
reaching the customer. Internal failure costs include the cost of repairing or replacing a defective product and
any discount given to the customer for purchasing the reworked product. External failure costs include all internal failure costs plus the cost
of shipping and handling and lost sales due to the effects on the company’s reputation. Since external failure
costs include all internal failure costs, it is assumed that external failure costs will be greater than internal failure costs.
Therefore, a company would prefer to fix a defective item before it is sold to the customer.

The first step in quality cost minimization is to determine a cost function for each of the four quality activities:
prevention, appraisal, internal failure and external failure. After estimating these quality costs, the company needs to determine what
level of external failure is acceptable. For example, the company discussed in the article manufactures a chemical used to
patch holes in plywood and has decided that a 1% defect rate in products shipped to customers was acceptable. A
higher defect rate would be disastrous to the company in terms of lost sales. Companies producing a product that, if defective, may have catastrophic
consequences, may decide that there is no room for any external failures and that each and very unit shipped to customers must either be made correctly in
initial production or be inspected and re-worked prior to being shipped out.

The next step is for the company to determine the optimal combination of prevention activities and appraisal
activities to ensure that the external failure rate does not exceed the
acceptable limits. The TQM approach would lead managers towards creating a process where all units are made
correctly during the initial production, thereby eliminating the need to re-work defective items. Most companies, however, find that creating such a system is
too expensive and will need to rely on the appraisal process to discover and correct defective units. These
companies can achieve the most cost-effective combination of prevention and appraisal activities at the point where the marginal cost of prevention is equal
to the negative of the marginal cost of internal failure. After this point, it is more costly to make a good unit that to repair a
defective unit. The company referred to above determined that the optimal level of prevention occurs at 10%
defects in initial production. In other words, it would be more costly for the company to concentrate their
efforts on producing less than 10% defects in initial production than to re-work these defective units. The
appraisal process must then identify enough defective units to bring the total external failure rate down to the acceptable limits.

The authors recognize that some companies may opt to produce all units correctly the first time as consistent with the TQM
approach. For those companies that find this approach to be too costly, the authors have provided guidance on
determining the optimal combination of prevention and appraisal activities. By analyzing the cost functions for the four quality
activities - prevention activities, appraisal activities, internal failure and external failure - a company can cost-effectively achieve a combination of
prevention and appraisal activities that will result in an acceptable external failure rate.